# Derivative of 3cosx

Derivative |
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d/dx(3 cos(x)) = -3 sin(x) |

Alternate form |

3/2 i e^(i x) – 3/2 i e^(-i x) |

Roots |

x = pi n, n element Z |

Series expansion at x=0 |

-3 x + x^3/2 – x^5/40 + O(x^6) (Taylor series) |

Indefinite integral |

integral -3 sin(x) dx = 3 cos(x) + constant |

Global minima |

min{-3 sin(x)} = -3 at x = 2 pi n + pi/2 for integer n |

Definite integral over a half-period |

integral_0^pi-3 sin(x) dx = -6 |

Definite integral mean square |

integral_0^(2 pi) (9 sin^2(x))/(2 pi) dx = 9/2 = 4.5 |